How to emit particles at intersection of faces (Scan animation)
Material
Dot pattern texture with appearance controled by Radial Blend texture.



Laser line is shrinkwrapped line, just for illustration, you will use your laser :)
Particles
They looks better, since there is not a deformation on surface curvature. I wanted to use the same Radial blend texture as factor for Emission, but I had some dificulties to get it work for particle system. So here is a version with particles emited from Shrinkwrapped line of vertices suggested by Rich Sedman
Works nice like real one in term - light string follows surface and keeps empty places where light cant touch surface (like in tail part).
Issue is distribution. I wasnt able to set even release particles from vertices.